We present a simple exact algorithm for the \is\ problem with a runtime bounded
by $O(\rt^n \poly(n))$. This bound is obtained by, firstly, applying a new
branching rule and, secondly, by a distinct, computer-aided case analysis.
The new branching rule uses the concept of satellites and has previously only
been used in an algorithm for sparse graphs.
The computer-aided case analysis allows us to capture the behavior of our algorithm
in more detail than in...